Following the discussions in [1]} and [2]} for the standard
NJL model, one must contruct the effective meson interaction
\(U_{\alpha \alpha ^{\prime }, \beta \beta ^{\prime }}\) , where all relevant degrees of freedom are subsumed in the indices \(\alpha , \alpha ^\prime , \beta , \beta ^\prime \) . The effective interaction is expressed in terms of the (proper) polarization insertion \(\Pi _{\lambda \lambda ^{\prime }, \mu \mu ^{\prime }}\) :
\(\begin{split}iU_{\alpha \alpha ^{\prime }, \beta \beta ^{\prime }}(k)&=iU^0_{\alpha \alpha ^{\prime }, \beta \beta ^{\prime }}(k)\\&+iU^0_{\alpha \alpha ^{\prime }, \lambda \lambda ^{\prime }}(k)[-i\Pi _{\lambda \lambda ^{\prime }, \mu \mu ^{\prime }}(k)]iU_{\mu \mu ^{\prime }, \beta \beta ^{\prime }}(k) .\end{split}\) 
